ON VARIOUS APPROACHES TO ASYMPTOTICS OF SOLUTIONS TO THE THIRD PAINLEVE EQUATION IN A NEIGHBORHOOD OF INFINITY

摘要

We examine asymptotic expansions of the third Painleve transcendents for αδ≠0 and γ = 0 in the neighborhood of infinity in a sector of aperture <2π by the method of dominant balance). We compare intermediate results with results obtained by methods of three-dimensional power geometry. We find possible asymptotics in terms of elliptic functions, construct a power series, which represents an asymptotic expansion of the solution to the third Painleve equation in a certain sector, estimate the aperture of this sector, and obtain a recurrent relation for the coefficients of the series.